Log-normal glide and the formation of misfit dislocation networks in heteroepitaxial ZnS on GaP

TL;DR

This study addresses how mismatch strain drives the formation of misfit-dislocation (MD) networks during ZnS/GaP (001) heteroepitaxy and whether SEM-based ECCI can quantify these networks across large areas. Using a two-chamber MBE process, ZnS films of 15–50 nm were grown and imaged by ECCI over many micrographs, with complementary HRXRD, AFM, and cross-sectional S/TEM to track strain, surface morphology, and MD/TD evolution. The results show no MDs below the critical thickness $h_c \approx 15$–$20$ nm, the appearance of MD segments near $h_c$, and increasing MD lengths and TD density at higher $h$, along with a roughening transition linked to surface terminating dislocations. The MD length distribution is consistently log-normal across directions and thicknesses, implying a normal distribution of activation energies for MD nucleation and TD glide, and the MD content quantitatively matches the HRXRD-measured strain relaxation. These findings validate ECCI as a statistically robust method for mapping dislocation networks and reveal anisotropic MD glide kinetics with implications for strain-engineered heteroepitaxy.

Abstract

Scanning electron microscopy (SEM) based electron channeling contrast imaging (ECCI) is used to observe and quantify misfit dislocation (MD) networks formed at the heteroepitaxial interface between ZnS and GaP grown by molecular beam epitaxy (MBE). Below a critical thickness of 15-20 nm, no MDs are observed. However, crystallographic features with strong dipole contrast, consistent with unexpanded dislocation half-loops, are observed prior to the formation of visible interfacial MD segments and any notable strain relaxation. At higher film thicknesses (20 to 50 nm), interfacial MD lengths increase anisotropically in the two orthogonal in-plane <110> line directions, threading dislocation (TD) density increases, and a roughening transition is observed from atomically smooth two-dimensional (2D) to a multi-stepped three-dimensional (3D) morphology, providing evidence for step edge pinning via surface terminating dislocations. The ZnS strain relaxation, calculated from the total MD content observed via ECCI, matches the average strain relaxation measured by high-resolution x-ray diffraction (HRXRD). The MD lengths are found to follow a log-normal distribution, indicating that the combined MD nucleation and TD glide processes must have a normal distribution of activation energies. The estimated TD glide velocity ($v_{g}$) along [$\bar{1}$10] is almost twice that along [110], but in both directions shows a maximum as a function of film thickness, indicating an initial burst of plasticity followed by dislocation pinning.

Figures (7)

• Figure 1: Characterization of surface morphology and strain state of epitaxial ZnS grown on GaP (001) by molecular beam epitaxy (MBE).(a) In-situ reflection high energy electron diffraction (RHEED) along [110] of (top) the GaP surface just prior to ZnS deposition, and (bottom) just after deposition of 50 nm ZnS film. (b) High-resolution x-ray diffraction (HRXRD) data (points) and dynamical diffraction fit (lines) for determining film thickness ($h$) and relaxation ($R$). (c) Morphology of epilayers at various thicknesses by atomic force microscopy (AFM).
• Figure 2: (a) Atomic resolution with Z-contrast (S/TEM HAADF) cross-sectional image of 15 nm ZnS film along [110] and (b) zoomed view of the same data set at the interface. (c) Chemically resolved image (EDS), and (d) line-cut extracted in the direction of the arrow of (c).
• Figure 3: Plan-view scanning electron microscopy (SEM) based imaging of misfit dislocation (MD) network formation in ZnS epilayers grown on GaP. (a) Electron channeling pattern (ECP) of ZnS/GaP and (b) indexed representation of Kikuchi lines. Electron channeling contrast imaging (ECCI) of ZnS/GaP films along diffraction vector, $g=$ ($\bar{2}$20) (c-f) and ($\bar{4}$00) (g-j) at each film thickness.
• Figure 4: Correlation between ECCI quantified defects, surface morphology and strain state. (a) ECCI image (Fig. 3(i)) of ZnS 25 nm thick epilayer on GaP identifying dipole features (DFs) and misfit dislocations (MDs) that are counted and measured in for every film thickness via image processing. The cartoon illustrates how the DFs are consistent with surface nucleated dislocation half loops from which MDs are thought to be generated. (b) Density ($\rho$) of DFs and threading dislocations (TDs) versus film thickness $h$. (c) AFM measured RMS roughness ($R_{q}$, red data) and island density ($\rho_i$, blue data) as a function of threading dislocation (TD) density ($\rho_{TD}$). (d) Average island height ($R_i$, black data) and average island aspect ratio ($R_i/d_i$, blue data) as a function of $\rho_{TD}$. (e) Strain relaxation state ($R$) of ZnS films as a function of $h$ determined from the ECCI measured MD density ($\rho_{MD}$) along [110] and [$\bar{1}$10] line directions), and independently estimated from fits to the HRXRD data of Fig. 1(b). Lines are guides to the eye
• Figure 5: Statistical analysis of misfit dislocation (MD) length measurements (see Fig. 3) for ZnS epilayers grown on GaP. (a) Number of MDs as a function of measured MD length ($L_{MD}$) binned every 25 nm. Data are plotted (bars) for three film thicknesses ($h$) and along both MD directions ($u$) with corresponding fits (lines) to a log-normal distribution. (b) The same data from (a) are replotted as a cumulative number of MDs plotted on a log-scaled x-axis, which enables two parameter fits of the data using the log-normal cumulative distribution function (CDF) plotted as lines.